how to you solve f^-5/(f^-3)^-1

Question

i need help with solving the above problem

 

Answer 1

Hi Kristen,

Using the rule of exponents:

(x^m)ⁿ = x^{m * n}

so, (f ^-3)^-1 = f ^(-3 * ^-1) = f ³ and so, the expression becomes:

f ^-5/ (f ^-3)^-1= f ^-5 / f ³

The rule of exponents  x^m / xⁿ = x^m-n  tells us that we can re-write the expression as:

f ^{-5 - (3)} = f ^-8 or

1/ f ⁸

since a negative exponent tells us that the term is below the division bar or the denominator of a fraction.

Hope this helps!

Answer 2

Kristen.... think of a negative exponent as a halo on a variable or number...if the halo is positive, then it is on the proper side of the division bar....if the halo is negative, then it is out-of-place....move it to the other side of the division bar...in your question above the top variable "f" has a (-5) exponent...so move it out of the numerator into the denominator and change the (-5) to a (+5)...its in the "proper place"...as for the f^-3 to the -1...use rule of exponents and it simplifies to f^3  ( -3 times -1 = +3).  Hence, we have eight f's in the denominator and a one in the numerator .... ANSWER is   1/f^8

 less wordy way to solve....use rules of exponents X^m/X^n  = X^(m-n)....f^-5-(3) = f^-8 = 1/f^8